Open AccessSHIFTED LEGENDRE FRACTIONAL PSEUDOSPECTRAL DIFFERENTIATION MATRICES FOR SOLVING FRACTIONAL DIFFERENTIAL PROBLEMS
Author(s) -
M. Abdelhakem,
Dina Abdelhamied,
Maryam G. Alshehri,
M. El-Kady
Publication year - 2021
Publication title -
fractals
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.654
H-Index - 44
eISSN - 1793-6543
pISSN - 0218-348X
DOI - 10.1142/s0218348x22400382
Subject(s) - legendre polynomials , mathematics , legendre wavelet , associated legendre polynomials , fractional calculus , legendre's equation , gauss pseudospectral method , legendre function , algebraic equation , orthogonal functions , differential equation , ordinary differential equation , mathematical analysis , convergence (economics) , orthogonal polynomials , pseudo spectral method , classical orthogonal polynomials , gegenbauer polynomials , fourier transform , computer science , nonlinear system , fourier analysis , artificial intelligence , economic growth , wavelet transform , quantum mechanics , discrete wavelet transform , physics , wavelet , economics
A new differentiation technique, fractional pseudospectral shifted Legendre differentiation matrices (FSL D-matrices), was introduced. It depends on shifted Legendre polynomials (SLPs) as a base function. We take into consideration its extreme points and inner product. The technique was used to solve fractional ordinary differential equations (FODEs). Moreover, it extended to approximate fractional integro-differential equations (FIDEs) and fractional optimal control problems (FOCPs). The novel FSL D-matrices transformed these fractional differential problems (FDPs) into an algebraic system of equations. Also, an error and a convergence analysis for that technique were investigated. Finally, the correctness and efficiency of this technique were examined with test functions and several examples. All the results were compared with the results of other methods to ensure the investigated error analysis.